The Force on a Magneto-spherical Particle Oscillating in a viscous Fluid Perpendicular to an Impermeable Planar Wall with Slippage

Abstract

The effect of a magnetic field and slip on the motion of a solid sphere moving perpendicular to an unbounded rigid wall in an unlimited viscous fluid is investigated. As the sphere vibrates perpendicularly to the rigid wall, its center line is accompanied by a low amplitude vibration. A slip condition is applied to the sphere surface, while a no-slip dynamic condition is applied to the wall. Additionally, a semi-analytical method and a numerical scheme using collocation are presented. Furthermore, we calculate the amplitude of the non-dimensional coefficients of drag force acting on the solid sphere using various values of frequency, separation, and magnetic parameters. In addition, streamlines are plotted. The results of the magnitude normalized drag force are compared with those in previous literature.